"코테베그-드 브리스 방정식(KdV equation)"의 두 판 사이의 차이
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이 항목의 스프링노트 원문주소==
Pythagoras0 (토론 | 기여) 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
Pythagoras0 (토론 | 기여) 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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| 1번째 줄: | 1번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 스프링노트 원문주소 | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 스프링노트 원문주소== |
* [[코테베그-드 브리스 방정식(KdV equation)|솔리톤]] | * [[코테베그-드 브리스 방정식(KdV equation)|솔리톤]] | ||
| 7번째 줄: | 7번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요 | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요== |
* any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift) | * any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift) | ||
| 23번째 줄: | 23번째 줄: | ||
| − | ==러셀(John Scott Russell)의 관찰 | + | ==러셀(John Scott Russell)의 관찰 == |
* Using a wave tank, he demonstrated four facts<br> | * Using a wave tank, he demonstrated four facts<br> | ||
| 37번째 줄: | 37번째 줄: | ||
| − | ==코테베그-드 브리스 방정식 (KdV equation) | + | ==코테베그-드 브리스 방정식 (KdV equation)== |
* <math>u_{xxx}=u_t+6uu_x</math> | * <math>u_{xxx}=u_t+6uu_x</math> | ||
| 56번째 줄: | 56번째 줄: | ||
| − | ==역사 | + | ==역사== |
* [http://www.ma.hw.ac.uk/%7Echris/scott_russell.html John Scott Russell and the solitary wave] | * [http://www.ma.hw.ac.uk/%7Echris/scott_russell.html John Scott Russell and the solitary wave] | ||
| 68번째 줄: | 68번째 줄: | ||
| − | ==메모 | + | ==메모== |
* http://docs.google.com/viewer?a=v&q=cache:dWzyEHjy6JsJ:kft.umcs.lublin.pl/kmur/download/prezentacje/solitons_my.ppt+soliton+ppt&hl=ko&gl=us&pid=bl&srcid=ADGEESi5cLc2o4aGrXBSQM9i6u_2MalwSshBjfJzoGv4FsWRYcdUPcXNvQhwXLG6RpQsnwlT0f5-UGFkKVJr14cvsGjY2zDOhqLc1bwORnRHVYCsbv08l5dgO9xFhgNO8D1Vg29R4SAJ&sig=AHIEtbRDvlbVm-kiG23Az3C2olliRZdB8Q | * http://docs.google.com/viewer?a=v&q=cache:dWzyEHjy6JsJ:kft.umcs.lublin.pl/kmur/download/prezentacje/solitons_my.ppt+soliton+ppt&hl=ko&gl=us&pid=bl&srcid=ADGEESi5cLc2o4aGrXBSQM9i6u_2MalwSshBjfJzoGv4FsWRYcdUPcXNvQhwXLG6RpQsnwlT0f5-UGFkKVJr14cvsGjY2zDOhqLc1bwORnRHVYCsbv08l5dgO9xFhgNO8D1Vg29R4SAJ&sig=AHIEtbRDvlbVm-kiG23Az3C2olliRZdB8Q | ||
| 79번째 줄: | 79번째 줄: | ||
| − | ==관련된 항목들 | + | ==관련된 항목들== |
* [[파동 방정식|파동방정식]] | * [[파동 방정식|파동방정식]] | ||
| 88번째 줄: | 88번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">수학용어번역 | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">수학용어번역== |
* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | * 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | ||
| 103번째 줄: | 103번째 줄: | ||
| − | ==사전 형태의 자료 | + | ==사전 형태의 자료== |
* [http://ko.wikipedia.org/wiki/%EC%86%94%EB%A6%AC%ED%86%A4 http://ko.wikipedia.org/wiki/솔리톤] | * [http://ko.wikipedia.org/wiki/%EC%86%94%EB%A6%AC%ED%86%A4 http://ko.wikipedia.org/wiki/솔리톤] | ||
| 112번째 줄: | 112번째 줄: | ||
| − | ==리뷰 | + | ==리뷰== |
* [http://kasmana.people.cofc.edu/SOLITONPICS/index.html An Introduction to Solitons] ,Alex Kasman | * [http://kasmana.people.cofc.edu/SOLITONPICS/index.html An Introduction to Solitons] ,Alex Kasman | ||
2012년 11월 1일 (목) 13:06 판
이 항목의 스프링노트 원문주소==
개요==
- any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift)
- Solitons were discovered experimentally (Russell 1844)
- analytically (Korteweg & de Vries, 1895)
- modelling of Russell's discovery
- 1-soliton solution
- numerically (Zabusky & Kruskal 1965).
- interaction of two 1-soliton solutions
- they discovered that solitons of different sizes interact cleanly
러셀(John Scott Russell)의 관찰
- Using a wave tank, he demonstrated four facts
- First, solitary waves have a hyperbolic secant shape.
- Second, a sufficiently large initial mass of water produces two or more independent solitary waves.
- Third, solitary waves cross each other “without change of any kind.”
- Finally, a wave of height h and traveling in a channel of depth d has a velocity given by the expression (where g is the acceleration of gravity), implying that a large amplitude solitary wave travels faster than one of low amplitude.
코테베그-드 브리스 방정식 (KdV equation)
- \(u_{xxx}=u_t+6uu_x\)
- 1-soliton 해의 유도
\(u(x,t)=f(x-ct)\)로 두자.
\(f'''= 6ff'-cf'\)
\(f''=3f^2-cf+b\)
\(f''f'=(3f^2-cf+b)f'\)
\(\frac{1}{2}(f')^2=f^3-\frac{c}{2}f^2+bf+a\)
역사
- John Scott Russell and the solitary wave
- http://www.google.com/search?hl=en&tbs=tl:1&q=
- Earliest Known Uses of Some of the Words of Mathematics
- Earliest Uses of Various Mathematical Symbols
- 수학사연표
메모
- http://docs.google.com/viewer?a=v&q=cache:dWzyEHjy6JsJ:kft.umcs.lublin.pl/kmur/download/prezentacje/solitons_my.ppt+soliton+ppt&hl=ko&gl=us&pid=bl&srcid=ADGEESi5cLc2o4aGrXBSQM9i6u_2MalwSshBjfJzoGv4FsWRYcdUPcXNvQhwXLG6RpQsnwlT0f5-UGFkKVJr14cvsGjY2zDOhqLc1bwORnRHVYCsbv08l5dgO9xFhgNO8D1Vg29R4SAJ&sig=AHIEtbRDvlbVm-kiG23Az3C2olliRZdB8Q
- http://www.springerlink.com/content/gr665351h46628j6/fulltext.html
- http://people.seas.harvard.edu/~jones/solitons/pdf/025.pdf
- http%3A%2F%2Fkft.umcs.lublin.pl%2Fkmur%2Fdownload%2Fprezentacje%2Fsolitons_my.ppt
관련된 항목들
수학용어번역==
- 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
- 발음사전
- 대한수학회 수학 학술 용어집
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
사전 형태의 자료
리뷰
- An Introduction to Solitons ,Alex Kasman
- any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift)
- Solitons were discovered experimentally (Russell 1844)
- analytically (Korteweg & de Vries, 1895)
- modelling of Russell's discovery
- 1-soliton solution
- numerically (Zabusky & Kruskal 1965).
- interaction of two 1-soliton solutions
- they discovered that solitons of different sizes interact cleanly
- First, solitary waves have a hyperbolic secant shape.
- Second, a sufficiently large initial mass of water produces two or more independent solitary waves.
- Third, solitary waves cross each other “without change of any kind.”
- Finally, a wave of height h and traveling in a channel of depth d has a velocity given by the expression (where g is the acceleration of gravity), implying that a large amplitude solitary wave travels faster than one of low amplitude.
- 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
- 발음사전
- 대한수학회 수학 학술 용어집
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
사전 형태의 자료
리뷰
- An Introduction to Solitons ,Alex Kasman